Based on fluid dynamics experiments and numerical simulations, we have developed a model of metal fragmentation in a magma ocean which is based on the idea that the interaction between turbulent fluctuations and the mean flow results in vigorous stirring and stretching of the metal phase. The metal phase topology is predicted to quickly evolve from a compact blob of metal (the impactor's core) toward metal sheets and ligaments, which can then fragment into drops due to a capillary instability. Heat and mass transfer between metal and silicates can be understood as a mixing problem for a scalar field (temperature or chemical composition) which is carried by both phases. We have developed what we think is a solid theoretical framework for modelling chemical and thermal equilibration during planetary core formation using a formalism inspired by recent advances made in the field of mixing theory, and developed laboratory experiments that have allowed us to characterise and model the time and spatial variability of the concentration field in the metal-silicate mixture.
In parallel, we have developed an experimental set-up allowing to study vertical and oblique impacts in liquid systems, which has allowed us to develop scaling laws for the amount of large scale silicate/metal mixing following a vertical impact. The model predicts significant dispersion of the metal phase by impact-related process. Together with the mixing model discussed in the first paragraph, this can be used to parameterise metal-silicates chemical interaction in geochemical models of core formation.
Using geochemical modelling of core formation, we have obtained theoretical bounds for the evolution during accretion of the pressure and temperature of equilibration, which are key ingredients for estimating the composition of the core and its initial heat content. Our approach allows to get rid of the usually made assumption of equilibration at a pressure which is a constant fraction of the core-mantle boundary pressure. Our bounds show that the equilibration pressure must have remained relatively low during the first ~80% of accretion, while much larger equilibration pressures (up to CMB pressure or higher) are allowed in the last ~20% of accretion. This is consistent with the idea that the final stages of Earth’s accretion have involved giant impacts.
Finally, we have developed a coupled thermal/geochemical modelling approach which allows to link the core heat content to the geochemical signature of core formation. The idea is to feed geochemical constraints on the metal/silicates equilibration pressure and temperature into a model of the thermal evolution of the metal phase to predict the primordial heat content of the core. According to this model, the core heat content correlates with the core composition. Interestingly, many geochemically consistent accretion histories yield core temperatures which are inconsistent with the constraints we have on the present-day core temperature. This provides a previously unexplored way of constraining the evolution of magma ocean depth and thermal state of the mantle during accretion.
